1. 9.5 Adding and Subtracting Rational Expressions 4/23/2014

2. Same Denominator: When adding or subtracting fractions with same denominators, add/subtract the numerators and keep the same denominator

3. Example 1 Add and Subtract with Like Denominators Perform the indicated operation. 2x2x 3 2x2x 5 + Add numerators and simplify. 2x2x 3 2x2x 5 + = 35 + 2x2x = 2x2x 8

4. Different Denominators: If the denominators are different, find the least common denominator (LCD).

5. Example 2 Find the LCD of Rational Expressions Find the least common denominator. a. 6x6x 1, 8x 38x 3 1

6. Example 2 Find the LCD of Rational Expressions Find the least common denominator. b. 1 2x 4 – 1 3x 9 +, 2x - 4 = 2(x – 2) 3x + 9 = 3(x + 3) 2: 2, 4, 6, 8… 3: 3, 6, 9, 12… LCD: 6(x-2)(x+3) (Take the LCM and multiply by the rest of their factors)

7. Example 2 Find the LCD of Rational Expressions Find the least common denominator. c. 3, x 2 – x x 2 4 –

8. Example 2 Find the LCD of Rational Expressions Find the least common denominator. x 1 + –, x 2x 1 + d.

9. Basic Example of Adding Fractions with different denominators. 4: 4, 8, 12, 16.. 3: 3, 6, 9, 12… LCD: 12 9 4 13

10. Example 3 Add with Unlike Denominators Perform the indicated operation. a. 2x2x 3 + x 2x 2 4 Find LCD :

11. Example 3 Add with Unlike Denominators Find LCD :

12. Checkpoint Add and Subtract with Unlike Denominators Perform the indicated operation. 2x2x 3 7. x 2x 2 2 + ANSWER 2x 22x 2 + 3x3x4

13. Checkpoint Add and Subtract with Unlike Denominators 8. 3 x 1 – x + + ANSWER x 2x 2 + 2x2x + 3 () x – 1 () x + 1 Perform the indicated operation.

14. Example 4 Add with Unlike Denominators

15. 9.5 p.497 #10, 12, 13, 15, 16-24even, 28, 30, 33, 37, 39 Homework:

16. Checkpoint Add and Subtract with Like Denominators Perform the indicated operation. 1. 3x3x 2 3x3x 4 + ANSWER x 2 2 2. x2 – x x2 – – ANSWER – 1 x 2x2x 4 + 3. x4 + – x3 – ANSWER x4 + x3 +

17. Subtracting Polynomials

18. Example 1 Subtract with Like Denominators Subtract. x x 3 + x 2 3 + – Subtract numerators. x x 3 + x 2 3 + – = x3 + x2 –

19. Checkpoint Extra Examples 2 1. x2 – x x2 – – ANSWER – 1 x 2x2x 4 + 2. x4 + – x3 – x4 + x3 +

20. Example 2 Subtract with Unlike Denominators Subtract. 2 x 2x 2 – – 1 x 2x 2 – x – 2 4

21. Checkpoint Add and Subtract with Unlike Denominators 11 – x 2x 2 – 1x + 1 ANSWER – x – 2 () x – 1 () x + 1 Perform the indicated operation.

22. Example 2 Subtract with Unlike Denominators Subtract. 2 x 2x 2 – – 1 x 2x 2 – x – 2 4 SOLUTION The factors of are and and the factors of are and. So, the LCD is. x 2x 2 – x – 2 () x – 2 () x + 1 x 2x 2 – 4 () x – 2 () x + 2 () x + 2 () x – 2 ( ) x + 1

23. Example 2 Subtract with Unlike Denominators Rewrite using LCD. = – 2 () x + 2 () x – 2 () x + 1 () x – 2 () x + 2 () x + 2 () x + 1 = Subtract numerators. x + 2 – 2 () x + 1 () x – 2 () x + 1 () x + 2 = Distributive property x + 2 – 2x2x () x – 2 () x + 1 () x + 2 – 2 Combine like terms. = x () x – 2 () x + 1 () x + 2 – () x + 1 2 x 2x 2 – – 1 x 2x 2 – x – 24 = 12 – Factor denominators. () x – 2 () x + 1 () x – 2 () x + 2

24. 9.5 p.497 # 11, 14, 29, 31, 32, 38,40, 41 Homework: